Too Many Sides, Too Little Information

Geometry Level 4

An equiangular quadrilateral ABCD has integral sides. A straight cut is made, which divides it into a triangle with integer sides, and a pentagon with a perimeter of 108 units. Given that four of the sides of the pentagon are 24, 18, 17 and 10 units, what is the area of the triangle (in square units)?

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